We believe that calculating FID using longrun samples from the EBM and data samples is an appropriate, if rough, measure of successful density modeling. We also believe that the field should move away from viewing log likelihood as a principled measure of successful density estimation, since the theoretical shortcomings described by [1]} are extremely common but unrecognized in practice across many probabilistic models, not just EBMs. Realism of longrun MCMC samples is a necessary but not sufficient condition for valid density modeling. We argue that investigating the visual quality of longrun samples is currently the most effective tool to study steady-state distributions, which are the primary object of interest for a probabilistic model. Though we use the FID metric as part of our evaluation, our density modeling experiments are best described as realism preservation experiments rather than image generation experiments.
